Ordering the Action Syntax: Inhibitory discrepancy
drives the temporal order of action sequences
Doekemeijer, R. A.1 roos@doekemeijer.nl
Dr. De Kleijn, R. E.1 kleijnrde@fsw.leidenuniv.nl
1Department of Cognitive Psychology, Leiden University, the Netherlands
June 20, 2019
Abstract
The serial order of an action syntax is principal to execute complex actions successfully and is reportedly driven by inhibitory processes. These processes regulate both the preceding action segment as well as all succeeding action segments in the sequence. In our study, we propose that the unidirectionality of serial order emerges from a discrepancy within these inhibitory processes. To test this premise, we determined (1) the independent effect of the directly preceding action segment, (2) the independent effect of the directly succeeding action segment, and (3) the difference between these two inhibitory effects on the degree of trajectory curvature of an ongoing (virtual) movement.
Overall, we found a tendency of the preceding action segment to repel the ongoing trajectory relative to the tendency of the succeeding action segment to attract it. These findings ultimately support the premised inhibitory discrepancy driving the temporal order of an action sequence. In fact, our findings suggest that the preceding action segment is inhibited more than the succeeding action segment in the sequence.
Nevertheless, we heed the power of our study and we commend further research on the independent inhibitory effects of the preceding and succeeding action segments on an ongoing action segment. Furthermore, we advocate research on the role of context-dependent and context-independent individual differences on the established inhibitory discrepancy driving the serial order of an action syntax.
Keywords: action sequencing, serial order, inhibition, movement trajectories, cursor trajecto-ries.
Introduction
Intuitively, humans perform complex actions by ordering them into a sequence of elementary ac-tion segments [1, 2]. For example, the abstract act of playing the piano can be viewed as a se-quence of pressing particular piano keys. Fun-damentally, the action segments, i.e., the so-called action syntax of the main act, is to occur in a unique temporal order to execute the main act successfully [3]. Currently, a well-known theory on the underlying mechanism driving this serial order of the action syntax proposes that action segments in the syntax are regu-lated by inhibitory processes [4]. These pro-cesses occur after a global excitation of all ac-tion segments, establishing the content of the action syntax, and are believed to ensure the temporal order of the sequence by (1) inhibiting all succeeding action segments and by (2) in-hibiting a preceding action segment upon com-pletion.
Both the premise of global excitation [5] as well as that of inhibition [6–8] have been ob-served in neuroscientific invasive studies on an-imals, suggesting a similar system in humans. However, this premise is hard to test due to measurement limitations accompanying human research; for ethical reasons, the invasive tech-niques used in the animal studies cannot be used in human studies. Nevertheless, Verschoor et al. (2015) inferred from infants’ eye gazes that infants inhibit the next, unexectuted ac-tion segment in the acac-tion sequence [2]. Fur-thermore, Behmer et al. (2017, 2018) recently demonstrated in a behavioural study [9] and a TMS/MEP study [10] that adults inhibited both the preceding and all succeeding letters when typing, showing an inverted V-shaped pattern of motor evoked potentials around the currently being executed (i.e., ongoing) action segment. Taken together, these findings sup-port the notion that (multiple) inhibitory pro-cesses drive the serial order of an action syn-tax.
However, a symmetry of the inhibition am-plitudes, as suggested by the inverted V-shaped pattern found by Behmer et al. (2018), fails to completely explain the mechanism underlying serial order. That is, supposing that the neural activity of the preceding and that of the suc-ceeding action segments are identical, inferen-tially, the next-to-be-executed action segment could be either the preceding or the succeed-ing action segment in the sequence. In other words, a symmetry of the two inhibitory pro-cesses should prompt either advancing or back-tracking in the sequence, whereas a discrepancy in the inhibitory processes would drive the se-rial order to be unidirectional. In the current study, we test this premise of an inhibitory discrepancy driving the temporal order of an action sequence. To do so, we adapt a cur-rent action-sequencing paradigm and dynami-cally assess the inhibitory processes.
Assessing inhibition
Conventional behavioral measures (e.g., reac-tion time and task accuracy) lack the abil-ity to capture the complexabil-ity of cognitive pro-cesses that unfold over time (i.e., the so-called dynamic processes) [11–14], whereas manual movement trajectories enable these dynamic processes to be measured accurately, non-invasively and inexpensively [14].
Particularly, the dynamic process of inhibi-tion is revealed by the degree of curvatures in manual movement trajectories: to-be-inhibited stimuli attract movement trajectories [15], in which the degree of trajectory curvature de-pends on, e.g., the spatial location [16, 17] and the salience of the stimuli [18–20]. More-over, this effect appears to be upheld for both real-time manual movements (e.g., pointing or reaching) as for virtual manual movements (e.g., directing a computer mouse) [21, 22]. In our study, we opted to establish inhibitory pro-cesses by employing the latter, due to its supe-rior accessibility [32].
The current study
To test the premise of inhibitory discrepancy as underlying mechanism driving the temporal order of the action sequence, we captured the curvatures of virtual movement trajectories. Specifically, we adapted Nissen and Bullemer’s (1987) action-sequencing task [24] to estab-lish the inhibitory effects of (1) the directly preceding action segment and that of (2) the directly succeeding action segment on the cursor trajectory curvature of an ongoing ac-tion segment. Overall, we expect these effects to be independent and dissimilar, signifying the premised discrepancy in the inhibitory processes.
Methods
Participants
A total of 24 participants were recruited from the Leiden University (Leiden, the Nether-lands). Participants who were left-handed or incapable to freely operate a computer mouse were excluded from the study.
The remaining participants were withheld information concerning the task sequence and concerning the recordings of their cursor posi-tions, in accordance to the ethical procedure founded by the Ethics Committee Psychology of Leiden University (CEP). At the end of the experiment, participants were debriefed about the recordings and were asked for explicit con-sent to use their data. Data of participants who did not consent was excluded.
Additionally, after the experiment, we ex-cluded participants who had not explicitly learned the sequence in the action-sequencing task (i.e., participants who failed to correctly reproduce the sequence). Ultimately, we in-cluded 18 participants (5 male and 13 female;
aged between 19 and 31 years old, M =
21.0, SD = 3.36) in our study.
Design
We implemented a single-session within-subjects design: each participant performed an action-sequencing task, a reproduction of the action sequence, and a working memory ca-pacity test. Here, participants’ cursor posi-tions were recorded solely during the action-sequencing task.
Importantly, as working memory capac-ity reportedly affects an individual’s abilcapac-ity to sequence actions [25, 26], we measured each participant’s working memory capacity and included it as a covariate in our analyses. Furthermore, we counterbalanced the action-sequencing task to account for the spatial prop-erties of the stimuli and randomly assigned the participants to either condition.
Apparatus
Computer specifications
All tasks were shown on a 17" computer mon-itor (LG Flatron 776 FM) with a refresh rate of 60 Hz. Moreover, the pointer acceleration, pointer trails, and enhanced pointer precision of the computer cursor were switched off.
Action sequencing task
Based on Nissen and Bullemer’s action-sequencing task [24], we created a computer task (in Pygame, Python 3.6) in which par-ticipants were to sequentially hit six stimuli using the computer cursor. The six stimuli were located at the upper left corner (1), upper center (2), upper right corner (3), lower left corner (4), lower center (5), and lower right corner (6) of the screen (see Figure 1). The two centered stimuli were vertically offset, hence appearing above the neighbouring corner stimuli.
Stimuli. The stimuli were 60px-sized,
1
2
3
4
5
6
Figure 1: Lay-out of the action-sequencing task, in which the center stimuli 2 and 5 preceded or succeeded the movements from corner stimulus 1 to 3 and from corner stimulus 4 to 6, respectively.
green according to a predefined sequence. The green-coloured stimulus defined the current target and reverted to red 1.0 second after being hit by the cursor. Then, after an inter-stimulus interval (ISI) of 1.0 second the next stimulus in the sequence turned green, cueing the participant to move the cursor to this next stimulus. Upon completion of the sequence, the sequence started anew. In total, the participant performed 3 blocks of 50 consecutive sequences, separated by breaks. Finally, we asked the participant to reproduce the invoked sequence to test their mastery of the action sequence.
Sequence. The predefined sequence of
the task was specifically designed to establish the effects of the preceding and the succeeding action segments on the curvature of an ongoing trajectory. To that end, the center stimuli either preceded or succeeded the left to right movement between two corner stimuli (see the dashed lines in Figure 1), invoking the effect of the preceding or that of the succeeding action segment, respectively. That is, according to Figure 1, stimulus 2 preceded or succeeded the
movement from stimulus 1 to 3; stimulus 5 the movement from stimulus 4 to 6. So, the invoked sequences were 1 − 3 − 2 − 5 − 4 − 6 and 4 − 6 − 5 − 2 − 1 − 3.
At the end of the action-sequencing task, we asked the participant to reproduce the sequence to establish their explicit knowledge on the ac-tion sequence. As previously menac-tioned, par-ticipants who failed to reproduce the sequence without cues were excluded from further anal-yses.
Working memory capacity test
To account for the effect of working memory capacity on the participant’s action sequencing performance, we measured the participants vi-suospatial working memory capacity using Bo, Jennet and Seidler’s (2011) task [25]. In this task, the participants were shown a range of (2 to 8) coloured circles for 100 ms, followed by a 900 ms fixation point, then 2000 ms of either the same or differently coloured circles. The participants were instructed to indicate whether the images were identical or different by means of button presses. After 140 trials,
the working memory capacity wj of each
partic-ipant j was computed from all trials using each trial’s number of circles n, the participant’s rate of correctly identified same coloured circles (i.e., hit rates Hj), and the participant’s rate of
in-correctly identified differently coloured circles (i.e., false alarm rates Fj), according to
wj(Hj, Fj) = 1 7 · 8 X n=2 ( n · [Hjn− Fjn]) (1) Procedure
Upon recruitment, participants were informed of the study (save the specifics of the task’s se-quence and the cursor trajectory recordings) and were requested to provide written con-sent to participate. Then, the participant was lead by the researcher to a secluded computer room, where the researcher launched the sequencing task. The instructions of the action-sequencing task were provided on the screen, in-dicating the participant to move the computer cursor to the target that turned green as fast and accurately as possible. During the breaks, the participants were instructed to rest their eyes and continue the task whenever they felt ready. At the end of the action-sequencing task, the participants were to reproduce the sequence without being cued. Upon completion, the re-searcher reentered the room to start the visu-ospatial working memory capacity task. Over-all, the tasks took approximately 35 minutes to complete. Conclusively, participants were de-briefed and were granted a (university-related) participation credit or a muffin as a reward.
Statistical analyses
To establish the inhibitory effects of the preced-ing action segment and that of the succeedpreced-ing action segment on an ongoing cursor trajectory, we computed the degree of the trajectory curva-ture as the average distance from each observed point within the trajectory to its projection on
the ideal trajectory, which is the straight line between a trajectory’s first observed point to its last observed point. Then, we predicted this distance in three multilevel analyses: the pre-ceding action segment (AS) analysis and suc-ceeding AS analysis addressed the independent effect of the preceding center target and that of the succeeding center target on the computed distance, respectively; the so-called differen-tial analysis addressed the proposed discrep-ancy between these two action segment effects. Overall, the first two analyses contained three multilevel models, i.e., two intercept-only mod-els and an unconditional growth model, and the last analysis included an additional uncondi-tional growth model. All models subsumed two levels to capture (first-level) trajectory effects and (second-level) participant effects.
Here, all analyses were conducted in a step-wise manner, so the models were nested and the previous models acted as baseline to the subsequent ones. More specifically, in all analy-ses, we expanded the best intercept-only model by adding the fixed effects of gender, age, and working memory capacity, thereby constituting the unconditional growth model. Then, in the differential analysis, we created a second un-conditional growth model by adding the fixed effect of the center target to the previous model. Note that the majority of the inspected effects were fixed; accordingly, we employed the max-imum likelihood method for all parameter esti-mations [27].
Conclusively, for each multilevel analysis, we determined the best model by evaluating the models’ trade-offs between simplicity and goodness-of-fit using AIC scores, BIC scores and log-Likelihood ratios. We expected the (last) unconditional growth models to outper-form their predecessors, ultimately reflecting the hypothesized independent and discrepant effects of the preceding action segment and the succeeding action segment on the trajectory curvature of an ongoing action segment.
Results
Preprocessing
Before conducting the stepwise multilevel anal-yses, the data was preprocessed. First, we ex-cluded (6) participants who had not explicitly mastered the sequence of the action-sequencing task, thus establishing our final sample of 18 participants. Note that this indicates that we had relatively low power to detect (second-level) participant effects [28]. Second, we ex-tracted all trajectories between stimulus 1 and 3 and between 4 and 6. Third, we removed all observations in the ISIs, and all erroneous or ir-regular trajectories (i.e., trajectories consisting of fewer than 14 observations or over 64 obser-vations). Overall, we included 2298 preceding center target and 2298 succeeding center tar-get trajectories in our analyses, each trajectory consisting of approximately 37 observed cursor positions.
Subsequently, we calculated the perpendic-ular distance from each cursor position p in the form [xp, yp] to its projection on the ideal
tra-jectory. Recall that this ideal trajectory was defined as the shortest line between the cursor’s starting position and its position upon hitting the target stimulus. So, for each trajectory i, we determined its corresponding ideal line of the form ax + by + c = 0 : b = −1, and estab-lished each observed point’s distance given its trajectory dpi, dpi([xp, yp], ai, ci) = ai· xp− yp+ ci q a2 i + (−1)2 (2)
This approach allowed the computed dis-tance to be both positive as well as negative, in-dicating observations positioned above and be-low the ideal trajectory, respectively.
Stepwise multilevel analyses
The parameter estimates and fit indices of all models within the conducted analyses are listed
in Table 1 and Table 2, respectively. In this sec-tion, we first outline the encompassed models’ compositions, then we discuss each model’s rel-ative goodness-of-fit, according to a Likelihood Ratio Test (LRT), in turn. We conclude this section by visually examining the assumptions of the final models.
Model compositions
We established a fixed-intercept model (I),
dij = γ00+ ij (3)
a subsequent random-intercept model (II), dij = γ0j+ ij
γ0j = γ00+ u0j
(4)
and an unconditional growth model (III) by adding the covariates gender gj, age aj, and working memory capacity wj,
dij = γ0j + γ10· gj+ γ20· aj
+ γ30· wj+ ij
(5)
Furthermore, in the differential analysis, we created a second unconditional growth model (IV) by adding the fixed effect of the center tar-get ctij to the previous unconditional growth
model,
dij = γ0j+ γ10· gj+ γ20· aj+ γ30· wj
+ γ40· ctij+ ij
(6)
Overall, dij represents the estimated average distance from point to ideal line of each tra-jectory i within a participant j, γn the model’s
estimate of parameter n, ij the error, and unj the residual between γnjand a participant’s ob-served parameter value.
Preceding and succeeding AS analyses The independent effect of the preceding ter target and that of the succeeding cen-ter target were first analyzed. We found a
Table 1: Parameter estimates of the models within each multilevel analysis, predicting the average distance from each observed point in a trajectory to its projection on the ideal trajectory.
Model1 (Intercept) Gender2 Age Working
memory Center target3 Preceding AS analysis I -0.51∗∗(0.12) II -0.54∗ (0.22) III -2.01 (1.78) -0.40 (0.48) 0.05 (0.07) 0.26 (0.26) Succeeding AS analysis I 0.29∗ (0.14) II 0.24 (0.44) III 3.69 (3.41) -1.63 (0.91) -0.06 (0.13) -0.87 (0.49) Differential analysis I -0.11 (0.09) II -0.15 (0.27) III 0.83 (2.17) -1.01 (0.58) -0.00 (0.08) -0.31 (0.31) IV 0.43 (2.17) -1.01 (0.58) -0.00 (0.08) -0.31 (0.31) 0.80∗∗(0.18) 1I : Intercept II : I + (Intercept | Participant)
III : II + Gender + Age + Working memory IV : III + Center target
2base: female.
3base: preceding center target. ∗
p < 0.05, ∗∗p < 0.001.
Table 2: Fit indices of the models within each multilevel analysis.
Model1 DoF Log-Likelihood AIC BIC
Preceding AS analysis I 2 -7214.27 14432.54 14444.02 II 3 -7203.45 14412.91 14430.12 III 6 -7202.21 14416.42 14450.85 Succeeding AS analysis I 2 -7555.83 15115.67 15127.15 II 3 -7488.53 14983.05 15000.27 III 6 -7486.11 14984.21 15018.65 Differential analysis I 2 -14805.40 29614.79 29627.66 II 3 -14754.51 29515.01 29534.31 III 6 -14752.70 29517.40 29556.00 IV 7 -14742.39 29498.78 29543.81 1I : Intercept II : I + (Intercept | Participant)
III : II + Gender + Age + Working memory IV : III + Center target
nonzero intercept both in the preceding p as well as in the succeeding s fixed-intercept model (I), tp(2297) = −4.37, p < 0.001; ts(2297) =
2.14, p < 0.05. Particularly, the preceding cen-ter target was associated with a negative dis-tance, indicating the average trajectory to be repelled by (i.e., curve away from) the center target. On the contrary, the succeeding center target was associated with a positive distance, thus indicating the average trajectory to be at-tracted to (i.e., curve toward) the center tar-get. In Figure 2, the (generalized) independent effects of the preceding and succeeding action segments on the ongoing cursor trajectories are illustrated.
The effect of the succeeding center target fell to non-significance in the random-intercept model (II), indicating that this effect did not uphold for all participants, t(2280) = 0.55, p = 0.58. This non-significance was similarly found in the following unconditional growth model (III), t(2280) = 1.08, p = 0.28. Additionally, this unconditional growth model estimated the contributions of gender g (base: female), age a, and working memory capacity w to be in-significant, tg(14) = −1.80, p = 0.09; ta(14) =
−0.46, p = 0.65; tw = −1.79, p = 0.09.
Ulti-mately, we concluded from two LRTs that the latter two models performed similarly, χ2(3) = 4.84, p = 0.18, and better than the first model, χ2(1) = 134.62, p < 0.001. Accordingly, the unconditional growth model (III) was uphold in the succeeding AS analysis.
With respect to the preceding AS analy-sis, we found the significance of the intercept as established in the fixed-intercept model (I) to be uphold in the random-intercept model (II), t(2280) = −2.49, p < 0.05. Neverthe-less, both the intercept and the covariates ap-peared insignificant in the subsequent uncon-ditional growth model (III), t0 = −1.13, p = 0.26; tg(14) = −0.84, p = 0.42; ta(14) =
0.74, p = 0.47; tw = 1.02, p = 0.33.
Over-all, the random-intercept model outperformed its predecessor, χ2(1) = 21.64, p < 0.001, and
was not outperformed by its successor, χ2(3) = 2.49, p = 0.48; so, we opted to retain the un-conditional growth model (III) in the preceding AS analysis.
Differential analysis
From the fixed-intercept model (I) and the random-intercept model (II) of the differen-tial analysis, we determined that the dis-tance between the observed and ideal trajec-tory was negligible for all subjects, tI(4595) =
−1.23, p = 0.22; tII(4578) = −0.56, p = 0.57;
χ2 = 101.78, p < 0.001. Furthermore, in nei-ther the first unconditional growth model (III) nor the second one (IV), we found any of the co-variates to significantly contribute to their re-spective model’s fit, III : t0(4577) = 0.20, p = 0.84, tg(14) = −1.76, p = 0.10, ta(14) =
−0.06, p = 0.96, tw(14) = −0.99, p = 0.34, χ2 = 1.171, p = 0.19; IV : t0(4578) = 0.38, p =
0.70, tg(14) = −1.76, p = 0.10, ta(14) =
−0.06, p = 0.96, tw(14) = −0.99, p = 0.34, χ2 = 1.90, p = 0.39. However, in the second uncon-ditional growth model, the center target (base: preceding center target) appeared to be positive and highly significant, tct(4577) = 4.54, p < 0.001. In other words, the succeeding center target invoked the distance to be more positive compared to the preceding center target. Over-all, we found this final model superior over all preceding models, χ2= 101.78, p < 0.001.
This effect of the center target may indicate that (1) the succeeding center target invokes a smaller negative distance than the preceding center target, ultimately suggesting a main re-pelling effect of the preceding center target, or that (2) the succeeding center target induces a greater positive distance than the preceding center target, thus implying a main attracting effect of the succeeding center target. Figure 3 shows that both propositions are supported by our data.
x p o s it io n o n s c re e n ( px ) 0 10 20 -20 -10 distance (x3 px) x p o s it ion o n s c re e n ( px ) 0 10 20 -20 -10 distance (x3 px) P re c e d in g a c tio n s e g m e n t S u c c e e d in g a c tio n s e g m e n t … P ar ticip an t’s a ve ra g e tr a ject o ry A ver ag e tr aject or y (9 5 % -CI ) Dat a -b a se d Rep e lling e ffe ct A tt ra ctin g e ffe ct G e n e ra liz e d A ve ra g e tr a ject o ry (9 5 % -CI ) Pr e c e di ng a nd s uc c e e di ng a c tio n s e gm e nt e ffe c ts on o ng oi ng c urso r tr a je c torie s Figure 2 : Th e effects of the preceding cen ter target (left) and succeeding cen ter target (righ t) on the cursor tra jectory of an ongoing action segmen t as found in our data (top) and as g eneralized to a main rep el ling or attracting effe ct (b ottom).
Preceding action segment
Succeeding action segment
n.s.
p < 0.001
distance (px)
- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6
Differential effect between preceding and succeeding action segments on trajectory curvatures
Figure 3: The relative effects of the preceding and succeeding action segments on the ongoing trajectory’s curvature, as measured by the averaged distance from the observed points within the trajectory to their projections on the ideal trajectory, for each participant separately (colored circles) and combined (grey bars, 95%-CI).
Assumptions of the final models
All final models assumed normality and ho-moscedasticity; accordingly, we employed Q-Q plots and scatter plots to visually test each model for any major assumption violations (see Appendix A and Appendix B, respectively). Although our sample size restricted our ability to identify violations, we determined that all final models solely exhibited slight non-normality.
Discussion
We examined virtual movement trajectories to test the premise that an discrepancy within the inhibitory processes drives the temporal order of an action sequence. Specifically, we exam-ined the effect of (1) the preceding action ment, that of (2) the succeeding action seg-ment, and (3) the inferential discrepancy be-tween these two effects on the cursor trajec-tory curvature of an ongoing action segment.
Overall, we tested each proposition in its corre-sponding multilevel analysis, assessing the de-gree of the trajectory curvature of the ongoing action segment as the average distance from the observed trajectory to the ideal trajectory. Ul-timately, we found a tendency for the preced-ing action segment to repel the ongopreced-ing cursor trajectory and a tendency for the succeeding action segment to attract it. Furthermore, we established the premised discrepancy between the effects of the preceding and succeeding ac-tion segments. We discuss each of these findings in turn, followed by our limitations and we con-clude with our suggestions for future research.
We established a tendency of the preced-ing action segment to repel the ongopreced-ing trajec-tory and a contrary tendency of the succeed-ing action segment to attract it, but lacked power to statistically detect them after ac-counting for individual differences (i.e., gender, age, and working memory capacity). Neverthe-less, the tendency of the succeeding action seg-ment to attract the ongoing trajectory is consis-tent with previous research, which has
repeat-edly demonstrated inhibited stimuli to attract ongoing trajectories [15, 21, 22]. The indepen-dent (repelling) effect of the preceding action segment on the ongoing action segment had, to our knowledge, thus far been unexplored, elect-ing our findelect-ing as pioneerelect-ing yet preliminary.
Furthermore, the discrepant tendencies of the preceding and succeeding action segments to respectively repel and attract the ongo-ing trajectory signify the expected discrepancy within the inhibitory processes that drive se-rial order. More particularly, the repelling ef-fect of the preceding action segment indicated that the preceding action was considered rela-tively nonsalient, while the attracting effect of the succeeding action segment indicated that the succeeding action was considered salient in the sequence [29]. Then, as inhibitory processes suppresses the salience of of stimuli [30], we pre-sume that the preceding action segment in the sequence was inhibited more than its succeed-ing counterpart.
Taken together, our findings support the no-tion of an inhibitory discrepancy between pre-ceding and succeeding action segments in the sequence. Particularly, we believe that this inhibitory discrepancy allows an individual to successfully execute an action sequence while being cognitively offline, i.e., without any in-formation from the environment. Tubau, Hom-mel, and Moliner (2007) noted that individuals either adopt stimulus-based control (i.e., rely-ing on external prompts) or plan-based con-trol (i.e., using an internally-generated plan of execution) to execute an action sequence [31]; based on the current findings, we propose that the internal mechanism enabling this plan-based control is the discrepancy between the in-hibitory processes of preceding and succeeding action segments.
Limitations and future directions
We note the limited power of our study to es-tablish individual-level effects and we advocate
further research to scrutinize the independent inhibitory effects of the preceding and succeed-ing action segments on the ongosucceed-ing action seg-ment by, e.g., increasing the sample size to over 50 [28]. To do so, we suggest the use of online experiment environments, such as Amazon Me-chanical Turk (MTurk).
Next, with respect to research using cur-sor trajectories, we advocate the implementa-tion of a baseline measure (e.g., a cursor tra-jectory unaffected by any stimuli) and/or the implementation of a training session. These im-plementations reportedly account for context-independent individual differences, such as an individual’s familiarity with directing the com-puter mouse, that may affect an individual’s cursor trajectories [32, 33].
Lastly, we regard the generalizability of our findings; our sample consisted of individuals who mastered the untold sequence in the task, i.e., those who adopted plan-based control, and we specifically propose that our findings may differ for individuals who employ stimulus-based control. Simply, the preceding and succeeding action segments can only be prop-erly inhibited if the individual is aware of the fact that they are the preceding and succeeding action segments in the sequence. Accordingly, we believe that our action segment effects depend on the individual’s cognitive control mode employed during the action-sequencing task. Overall, we recommend further re-search on the dependency of our findings on context-dependent individual differences, such as employed control mode.
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Appendices
A
Assumption tests for normality
0 0 0 1 -1 -1 -2 1 2 3 1 2 -1 0 -1 1 0 -1 1 0 -1 1 P re c e d ing A S a n a ly s is S u c c e e d in g A S a n a ly s is D if fe re n tia l a n a ly s is Data quantiles N o rm a l th e o re tic a l q u a n til e s
Norm
a
li
ty
of
the
d
a
ta
Figure 4: Normalit y of the second-lev el data as em plo y ed in the prece ding action segmen t analysis (left ), succeeding action segmen t analysis (middle), and differen tial analysi s (righ t).B
Assumption tests for homoscedasticity
-100 -50 0 50 P re c e d ing a c tion s e g m e n t S u c c e e d in g a c tio n s e g m e n t d is ta n c e (px )Hom
os
c
e
da
s
tic
ity
of
the
d
a
ta
,
firs
t-le
v
e
l
Figure 5: Homescedasticit y of the (first-lev el) tra jectory da ta as emplo y ed in the differen tial analysis.femal e mal e
